How do you compare two relationships when they have different types of growth?

For examplecompare the growth of t=2x

to the growth of t=2x

In this lesson you will learn to compare linear and geometric growth by creating and solving

equations.

Let’s Review

A linear sequence has a common difference between terms.

2, 4, 6, 8, 10, . . .

A geometric sequence has a common ratio between terms.2, 4, 8, 16, 32, . . .

+2 +2 +2 +2

×2 ×2 ×2 ×2

Core Lesson

How do I want to get paid?Payment Plan A: Start out with $20

and earn $5 per day

ORPayment Plan B: Earn $1 the first

day and double my earnings every day thereafter

Core Lesson

Payment Plan A:25, 30, 35, . . .

Payment Plan B:1, 2, 4, . . .

+5

+5

5(n-1) + 25

x 2 x 2

(1)(2)n-1

5(5) + 20 = 45

(1)(2)5-1 = 16

5n+20

Core Lesson

5n + 20 25, 30, 35, 40, 45, 50, 55, 60

(1)(2)n-1 1, 2, 4, 8, 16, 32, 64, 128

5(7) + 20 = 55

(1)(2)6 = 64

Plan A:

Plan B:

Starting in the 7th day, you will earn more money with Plan B.

In this lesson you have learned to compare linear and

geometric growth by creating and solving equations.

Guided Practice

I am making a pattern with regular pentagons. Each new pentagon I add I place next to another pentagon so that the sides meet.

I make another pattern with triangles in which I place them point-to-point with each other and count the total number of outer edges.

Will there ever be a time when I will have the same number of outer edges in both patterns?

Guided Practice

Pentagons:

5, 8, 113(n – 1) + 53n + 2

Triangles: 3, 6, 93(n – 1) + 33n

Extension Activities

• The sixth term of an arithmetic sequence is 17. The tenth term is 33. What is the first term? Which term of the sequence will be equal to 52?

• The third term of a geometric sequence is 4, and the 6th term is 32/27. What is the 5th term?

Extension Activities

Suppose every student in your math class shakes hands with every other member of your class. Write a rule to describe this situation, and find the minimum number of handshakes required.

Extension ActivitiesConsider the four squares to the right. Calculate the area of each square, and find the equation to model the change. Calculate the total area of the four squares using your equation. If the process of adding squares with half the perimeter of the previous square continued indefinitely, what would the total area of all the squares be?

1

1

½

½

¼

¼

⅛⅛

Quick Quiz

My friend and I each put $20 in a savings account. Her savings account will give her $1 interest each day. My savings account will give me 3% compound interest each day. Who has the better deal?

Quick Quiz

Suppose you are stacking boxes in levels that form squares. The numbers of boxes in successive levels form a sequence as shown at right. How many levels will you need to have if you are stacking a total of 285 boxes?